Digamma

The digamma function $\psi \colon \mathbb{C} \setminus \{0,-1,-2,\ldots\} \rightarrow \mathbb{C}$ is defined by $$\psi(z) = \dfrac{\mathrm{d}}{\mathrm{d}z} \log \Gamma(z) = \dfrac{\Gamma'(z)}{\Gamma(z)}.$$

• 

  Graph of $\psi$.

• 

  Domain coloring of $\psi(z)$.

Properties

Partial derivative of beta function
Digamma at 1
Digamma functional equation
Digamma at n+1

See Also

Gamma function
Polygamma function
Trigamma function

References

• 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.7 (1)$
• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $6.3.1$